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OnTheOtherHandle comments on Harry Potter and the Methods of Rationality discussion thread, part 26, chapter 97 - Less Wrong
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I would have loved to read a counterfactual HPMOR with Bones in the role of McGonagall (or McGonagall with the personality of Bones). It's true that her personality makes more sense in an Auror than a teacher, and that means we don't get to see her very much. But then again, virtually every major male authority figure in Hogwarts looks like he should belong in an elite war chamber rather than a classroom. Seriously, what are these people doing running a boarding school?
Draco seems to believe that Hogwarts is an impregnable fortress, a secure base for whatever power Dumbledore wants to project. Headmaster of Hogwarts appears to be a title awarded by the Wizengamot, which also elects the Chief Warlock, and Draco regards it as a significant increment to the power of the Chief Warlock. Its function as a boarding school may be secondary and incidental. :)
Hogwarts is more like a university than most boarding schools.
Hogwarts is the entire British magical education system (with the exception of some private tutors). Controlling education is not optional for people who want to control a country. The fact that education is all centralized the most powerful fortress just makes it even more important to control.
Do we know this for a fact?
Objections:
Going to Hogwarts is prestigious, meaning there must be lower-status options available.
Hogwarts regularly hires apparently British replacement teachers, most of them with at least the appearance of educational experience. It is improbable that said experience comes exclusively from abroad or from being a private tutor.
There are too few pupils at Hogwarts to account for the entire underage wizarding population, given the size of the overall wizarding population and assuming the majority of wizards' children are also wizards (not to mention having to factor in Muggleborns).
It seems improbable that the booming school equipment business of Diagon Alley survives on one school's worth of customers, especially if most of them only shop once a year.
If most of the population of magical Britain have been through the same school, we would expect an extremely high degree of social interconnectedness, with most people knowing everyone of the same age at least by sight. There's no evidence of this.
On the other hand,
It is implied that letters coming on one's 11th birthday can only come from Hogwarts.
If one is expelled from Hogwarts, one is forbidden from practising further magic altogether.
No other British schools, or pupils or graduates thereof, are ever mentioned in canon that I can remember.
Canon is fairly clear that Hogwarts is the only game in Britain. It also leads to glaring inconsistencies in scale which you just pointed out. (Rowling originally said that Hogwarts had about 700 students, and then fans started pointing out that that was wildly inconsistent with the school as she described it. And even that's too small to make things really work).
But the evidence, from HP7 (page 210 of my first-run American hardback copy):
Lupin is talking about Voldemort's takeover of Wizarding society, to Harry and the others.
"Most wizards" in Britain were educated at Hogwarts, and the exceptions were homeschooled or sent abroad. It's really hard to read that to imply that there's another British wizarding school anywhere.
It didn't seem to me there were so much school equipment business. If you look at the shops Harry went to the first year, it's a dress shop, a book shop, a wand shop, a potion ingredient shop, a broomstick shop, a pet shop, ... none of them sound dedicated to school equipment. They probably have a lot of school equipment in stock/display during august, like supermarkets do here too, but continue selling their goods to adult wizards the rest of the time.
The rest of your objections do hold, but I just fold it into "canon HP isn't very consistent" suspension of disbelief... of course, it makes things tougher for EY when he's making a consistent version of it. But that's part of what makes HPMOR funny/interesting.
I took the implication from reading the books that Rowling had different ideas at different times whether there were intended to be multiple schools of magic in Britain or not. It was referred to in the beginning as the "best" school in Britain, but by the end of the series, the Voldemort-run Ministry instituted mandatory Hogwarts attendance for all youth, and a character remarked that parents had at least had the option of homeschooling their children before.
The Magical economy generally doesn't seem to make a lot of sense. In canon it seems like every witch/wizard works for the Ministry, Hogwarts, or for a small restaurant or shop. I think wizards can pretty much conjure every basic material into existence except food and gold. That does leave an interesting question of where magical Britain is getting its food and gold from. There might be some witch/wizard farmers out there that we never hear about, or they could be just stealing food from muggles. Maybe the ministry sanctions some small scale trade between the magic/muggle world?
well... In cannon, the weaselys have a garden...and you can enlarge food with magic, though rowling never specifies what the multiplicative limit is. (it is STRONGLY implied there is one, though. seventh book.)
So a little bit of gardening by the women goes a long way, though it may only be poor families that actually resort to it.
It doesn't seem too implausible for them to have a law saying something along the lines of "a person who has been expelled from one magical school may not be admitted to any other magical school".
On the topic of illogical career paths, Bones has a real job that requires being a very good auror, rather than being an errand-boy for Dumbledore, as Moody seems to be.
And as for "what are these people doing running a boarding school", they run a school based on reward and (mostly) punishment, rather than the growth of their pupils; they teach a rigid curriculum that seems to have remained unchanged for centuries, in spite of advances in both the magical and muggle worlds; and they socially condition people into narrow roles, largely defined by negative attitudes towards others, based solely on the House a piece of fabric sorts them into.
To be fair, that's more support than Muggles give students choosing a major in college.
As a point of accuracy, it's been stated a couple of times that Hogwarts is meant to follow the Ministry-mandated curriculum, so this one is not entirely "these people"'s fault.
Thanks for the correction.
Source?